YES, this can happen.
Several years ago, I fell going "up" the stairs. I put my hands out to catch my fall, and my thumb nail dragged on the carpeting of a riser and lifted all the way to the lunula.
I cut it as short as possible and kept a bandaid on most of the time to keep the rest from tearing off.
Shortly after, I had a greenie under my nail, in the area separated.
(because water gets in there, and you can't dry it out:irked
I went to the DR, and received both and oral and topical prescription.
Neither worked. Darn thing just kept growing, and the oral medication had nasty side effects and risks (Lamasil).
I purchased Melaleuca tea-tree oil, applied that so that it ran under the nail into the affected area. Did this 2 - 4 times daily.
Bingo!
Greenie fixed.
It took 6mths to a year for my thumbnail to grow back properly.
hth's